chapter 3: prsentation of data

PRESENTATION OF DATATextual, Tabular, Graphical

A. TEXTUAL PRESENTATION OF DATAdata presented in paragraph or in sentences

includes: enumeration of important characteristicsemphasizing the most significant featureshighlighting the most striking attributes of the set of data

B. TABULAR PRESENTATION OF DATA

The Frequency Distribution Tablethis is a table which shows data arranged into different classes and the number of cases which fall into each class


Ungrouped Frequency Distributionmeans there is only one category per row

used if the range of the set of data is not so wide, for instance 10 or less

UNGROUPED FREQUENCY DISTRIBUTION

Year Level Number of Students (f)

Freshman 350

Sophomore 300

Junior 250

Senior 200

N = 1, 100

Table 3.0Distribution of Students in ABS High

SchoolAccording to Year Level

Source: ABS High School Registrar

Row

C

lass

ifier

Table number

Table Title

Column Header

Source Note

FOR EXAMPLE:

Construct a grouped and an ungrouped frequency distribution tables for the age of 50 service crews at Jollimee Restaurant

18 19 19 25 20 21 18 22 18 1925 18 21 24 25 22 18 23 24 1918 21 23 20 24 23 19 21 23 2020 21 22 24 23 25 21 20 22 2019 19 18 21 21 19 24 21 21 21

FOR EXAMPLE:The Ungrouped Frequency Distribution Table

for the Age of 50 Service Crews at Jollimee

Age Frequency Percentage Frequency

18 7 0.1400

19 8 0.1600

20 6 0.1200

21 11 0.2200

22 4 0.0800

23 5 0.1000

24 5 0.1000

25 4 0.0800

N = 50


Grouped Frequency Distributionmeans there are several categories in one row

used if the range of the set of data is so wide, for instance 11 and above

FOR EXAMPLE:The Grouped Frequency Distribution Table

for the Age of 50 Service Crews at Jollimee

Age Frequency Percentage Frequency

18 - 19 15 0.3000

20 - 21 17 0.3400

22- 23 9 0.1800

24 - 25 9 0.1800

N = 50

class

in

terv

als

lower limits LL

upper limits UL Class width (i) = UL – LL + 1


Simple Frequency Distribution Tableconsists only of class interval and frequency

FOR EXAMPLE:

Construct an ungrouped frequency distribution tables for the test scores of 50 students in Statistics

43 35 40 9 25 30 18 17 50 1235 46 10 36 33 37 41 21 20 3142 27 28 31 28 19 18 13 28 1626 13 4 48 40 48 40 39 32 3234 29 30 20 26 15 14 10 38 35

FOR EXAMPLE:A Simple Grouped Frequency Distribution for the Test Scores of 50 Students in Statistics

Class Interval(c. i) Tally Frequency (f)

4 - 9 II 2

10 - 15 IIII - II 7

16 – 21 IIII - III 8

22 – 27 IIII 4

28 – 33 IIII – IIII – I 11

34 – 39 IIII – III 8

40 – 45 IIII – I 6

46 – 51 IIII 4

N = 50


Complete Frequency Distribution Tablehas class mark or midpoint (X), class boundaries (c.b), relative frequency or percentage frequency and the less than cumulative and the greater than cumulative frequencies.

COMPLETE FREQUENCY DISTRIBUTION TABLE

The Range (R)The difference between the highest and the lowest score

R = Hs - Ls


The Class Interval (c.i)A grouping or category defined by a lower limit an upper limit


The class boundaries (c.b)It is half a unit below the LL and half a unit above the UL

If the unit is one; a half unit is 0.5If the unit is 0.1; half a unit is 0.05


The class mark or Midpoint (x)Average of the upper and lower limits that is

X = UL + LL

2


The class size (i)the difference between the upper class boundary and the lower class boundary of a class interval


The relative frequency (rf)Is obtained by dividing the frequency of each class by N


The less than cumulative frequency (<cf) and the greater than cumulative frequency (>cf)

are obtained by cumulating the frequency (f) from top to bottom and bottom to top respectively

STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION

1. Determine the Range.

R = Highest score – Lowest score

= 90 – 51

= 39

FOR EXAMPLE:

the test scores of 50 students in Statistics

51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83


2. Determine the desired class interval. The ideal number is somewhere between 5 and 15.

c.i = 8 (researcher’s choice)

FOR EXAMPLE:


51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83


3. Determine the approximate size or class width of class interval.

i = Range/ Class Interval

= 39/8

= 4.875

= 5 (rounded to whole number)

FOR EXAMPLE:


51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83


4. Construct a frequency table by making the class intervals starting with the lowest value in the lower limit of the first class interval then add the computed class size to obtain the lower limit of the next class interval.


5. Write the obtained frequency from each class interval by counting the tallied form.


6. Determine the class mark of each class interval

X = lower limit + upper limit

2


7. Determine the class boundaries or class limits by subtracting 0.5 from every lower limit and adding 0.5 from every upper limit.

FOR EXAMPLE:


51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83

FOR EXAMPLE: the test scores of 50 students in Statistics

Class Interval Tally Frequency Class Mark

51-55 IIII 4 53

N = 50

81-85

76-8071-75

66-70

61-65

56-60

86-90

IIII

IIII-IIIIII - IIII

IIII-IIII

IIII

III

IIII-III

5

79

10

4

3

8

83

7873

68

63

58

88

FOR EXAMPLE:


43 35 40 9 25 30 18 17 50 1235 46 10 36 33 37 41 21 20 3142 27 28 31 28 19 18 13 28 1626 13 4 48 40 48 40 39 32 3234 29 30 20 26 15 14 10 38 35

COMPLETE FREQUENCY DISTRIBUTION TABLEClass Interval(c.i)

Frequency(f)

Class Mark(X)

Class Boundary(c.b)

Relative Frequency (rf)

Less than Cumulative Frequency(<cf)

Greater than Cumulative Frequency(>cf)

4 - 9 2 6.5 3.5 – 9.5 .0400 2 50

10 - 15 7 12.5 9.5 – 15.5 .1400 9 46

16 – 21 8 18.5 15.5 – 21.5 .1600 17 40

22 – 27 4 24.5 21.5 – 27.5 .0800 21 32

28 – 33 11 30.5 27.5 – 33.5 .2200 32 21

34 – 39 8 36.5 33.5 – 39.5 .1600 40 17

40 – 45 6 42.5 39.5 – 45.5 .1200 46 9

46 – 51 4 48.5 45.5 – 51.5 .0800 50 2

N = 50


The Contingency Tableshows the data enumerated by cell

EXAMPLE:

CHOICE/SAMPLE

MEN WOMEN CHILDREN TOTAL

Like the program

50 56 45 151

Indifferent 23 16 12 51

Do not like the program

43 55 40 138

Total 116 127 97 340

The Contingency Table for the Opinion of Viewers on the New TV Program

C. GRAPHICAL PRESENTATION OF DATA

A graph add life and beauty to one’s work, but more than this, it helps facilitate comparison and interpretation without going through the numerical data

THE GRAPHS

1. Bar Chart:@ a graph represented by either

vertical or horizontal rectangles whose bases represent the class intervals and whose heights represent the frequencies.

@ it is used for discrete variables

BAR CHART

10 to 14

20 to 24

30 to 34

0 2 4 6 8 10 12

The Bar Chart for the Number of Stamps Collected by 35 StudentsSeries 2 Series 1

Base: Class IntervalHeight: Frequency

c.if

10-14320-241230-344

THE GRAPHS

2. Histogram:@ a graph represented by vertical or

horizontal rectangles whose bases are the class marks and whose heights are the frequencies.

@ it is used for continuous variables

HISTOGRAM

12 17 22 27 32 370

2

4

6

8

10

12

The Histogram for the Ages of 35 Aerobics Students

Base: Class Mark Height: Frequency

c.i fX

10-1431220-24122230-34432

THE GRAPHS

3. Frequency Polygon:@ this is a line version of the

histogram

@ it is a line whose bases are the class marks and whose heights are the frequencies

@ it is used for continuous variables

FREQUENCY POLYGON

10 15 20 25 30 35 40

3

12

4

The Frequency Polygon for the Ages of 35 Aerobics Students

Axis Title

Axis

Tit

le

Base: Class Mark Height: Frequency

c.ifX

10-14312

20-241222

30-34432

FREQUENCY POLYGON

0 5 10 15 20 25 30 35 40

3

12

4

9.514.5

19.524.5

29.534.5

39.5

The Less than Ogive for the Ages of 35 Aerobics Students

Axis Title

Base: Lower Class Boundary Height: <cf

<Ogivec.b

<cf-9.5

09.5-14.5 314.5-19.5 919.5-24.5 2124.5-29.5 2829.5-34.5 3234.5-39.5 35

FREQUENCY POLYGON

35 32 28 21 9 3

39.5

34.5

29.5

24.5

19.5

14.5

The Greater than for the Ages of 35 Aerobics StudentsAxis Title

Base: Lower Class Boundary Height: >cf

>Ogivec.b

>cf-9.5

09.5-14.5 314.5-19.5 919.5-24.5 2124.5-29.5 2829.5-34.5 3234.5-39.5 35

THE GRAPHS

4. Pie Chart:@ a circle graph showing the

proportion of each class through the relative or percentage frequency

PIE CHART

0.08

0.31

0.1

Base: Class IntervalHeight: Frequency

c.ifX

10-14312

20-241222

30-34432

THE GRAPHS

5. Pictograph:@ sometimes called pictogram

@ uses small pictures or figures of objects called isotopes n making comparisons. Each picture represents a definite quantity.

chapter 3: prsentation of data

Education

frequency table

distribution of students

cumulative frequency

tally frequency f

relative frequency rf

class width of class

class mark

class size